This quantity gives a direct measure of irreversible processes. In a compact form In its general form. The first term on the second member expresses the heat flow outside the cell, while the second one results from the exchange of matter with the intercellular environment. In order to find the heat and mass flow appearing in the expression of the RIEDP given in equations 1 and 2 , we employ the well-known heat and mass transport equations.

We consider a rectangular frame xyz with the origin in the center of the cell and we suppose that the flow direction is along x see Fig. Concerning the heat diffusion, it is mainly due to a conduction transport neglecting the convection transport present to a much lesser extent inside a typical cell and the term of heat source.

Hence, it is. We are grateful to S. Gangi, A. Strazzanti and F.

## Introduction to Thermodynamics of Irreversible Processes, Ilya Prigogine

Borziani for helpful discussion and kind support in this research activity. We thank Domenico Romolo for his graphical support in making Fig. This work is dedicated to the memory of Ilya Prigogine in occasion of his th birth anniversary. All authors contributed to the analysis of the results. Electronic supplementary material. Supplementary information accompanies this paper at doi Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

National Center for Biotechnology Information , U. Sci Rep.

## Introduction to Thermodynamics of Irreversible Processes - PDF Free Download

Published online Aug Zivieri , 1, 2 N. Pacini , 3 G. Finocchio , 2 and M. Carpentieri 4. Citelli 6, Catania, Italy Find articles by N. Author information Article notes Copyright and License information Disclaimer. Zivieri, Email: ti. Corresponding author. Received Mar 30; Accepted Jul This article has been cited by other articles in PMC. Abstract In living systems, it is crucial to study the exchange of entropy that plays a fundamental role in the understanding of irreversible chemical reactions.

Introduction The irreversible processes in living systems are fundamental for determining the autopoietic life development and lead to entropy production in living systems 1 — 3. Model for the calculation of the rate of entropy in living systems We have studied the cell as an open thermodynamic system in local equilibrium. Application of the rate of entropy model to glucose catabolism in normal and cancer breast cells We have applied the general model, described in the previous section, to glucose catabolism in a typical epithelial breast tissue.

Open in a separate window. Figure 1. Figure 2. Table 1 Chemical potentials and diffusion coefficients for the chemical species involved in glucose catabolism for cell respiration and lactic acid fermentation. Figure 3. Discussion According to the described model, we can draw important conclusions about the cell behaviour during glucose catabolism in terms of entropy production. Methods Basic principles Let us consider an open system cell that exchanges energy and matter with the environment. Diffusion equations In order to find the heat and mass flow appearing in the expression of the RIEDP given in equations 1 and 2 , we employ the well-known heat and mass transport equations.

Electronic supplementary material Supplementary Information 1. Author Contributions R. Notes Competing Interests The authors declare that they have no competing interests. Footnotes Electronic supplementary material Supplementary information accompanies this paper at doi References 1. Microscopic theory of irreversible processes. Lucia U. Phenomenological theory of ontogenesis. Luisi PL.

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### What is a Reversible Process?

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Prigogine, I. Far to be limited to students having to learn the subject, this impression is sometimes mentioned by specialists themselves who confess not being totally sure of the consistency of the thermodynamic theory, despite the fact that its practical usefulness is indisputable. The present paper deals with this interesting question and leads to the idea that there is an imperfect convergence between the way of using the thermodynamic tool and the way of understanding its significance.

Illustrated by a very simple example, the discussion can be followed by every scientist having the fundamental basis in thermodynamics. The suggested hypothesis is that the Einstein mass-energy relation is closely associated to the concept of entropy, opening a link between thermodynamics and relativity. Related Articles:. Date: March 24, Date: July 29, Code Switching in Sons and Lovers.